library(MASS)
#data(wtloss)
attach(wtloss)

# Plot the data to get an idea of what it looks like:
#
plot(Days, Weight, xlab='Days', ylab='Weight')
grid()

# Guess at the paramters:
#
n = dim(wtloss)[1]
beta1 = Weight[1] - Weight[n]

target = mean(c(Weight[1], Weight[n]) )
target_indx = which.min(abs(Weight - target))
beta2 = Days[target_indx]

beta3 = Weight[n]

fit = nls(Weight ~ beta1 * 2^(-Days/beta2) + beta3,
          data=wtloss, 
          start=c(beta1=beta1, beta2=beta2, beta3=beta3),
          trace=TRUE)
print(summary(fit))

if( !require('investr') ){
    install.packages('investr', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(investr)

plotFit(fit)
grid()